19 papers
Determining the Complexity of Chromatic Sum in Classes Defined by a Set of Forbidden Graphs
Clément Dallard, Daniël Paulusma, Erik Jan van Leeuwen
The Chromatic Sum problem asks, given a graph and an integer , whether admits a colouring with sum . We study the complexity of Chromatic S…
Optimal b-Colourings and Fall Colourings in -Free Graphs
Jungho Ahn, Tala Eagling-Vose, Felicia Lucke +3
In a colouring of a graph, a vertex is b-chromatic if it is adjacent to a vertex of every other colour. We consider four well-studied colouring problems: b-Chromatic Number, Tight…
Identification to Subclasses of Chordal Graphs
Petr A. Golovach, Laure Morelle, Daniël Paulusma
An identification of two vertices and in a graph replaces them with a new vertex whose neighborhood is the union of the neighborhoods of and . We study the {\sc ${\c…
On Detecting -Induced Minors for Small
Tala Eagling-Vose, Barnaby Martin, Daniël Paulusma +1
We consider the -Induced Minor problem: for a fixed graph~, decide whether a given graph contains as an induced minor. While the problem is known to be NP-complete fo…
Steiner Forest for -Subgraph-Free Graphs
Tala Eagling-Vose, David C. Kutner, Felicia Lucke +4
Our main result is a full classification, for every connected graph , of the computational complexity of Steiner Forest on -subgraph-free graphs. To obtain this dichotomy, we…
Colouring Graphs Without a Subdivided H-Graph: A Full Complexity Classification
Tala Eagling-Vose, Jorik Jooken, Felicia Lucke +2
We consider Colouring on graphs that are -subgraph-free for some fixed graph , which are graphs that do not contain as a subgraph. To classify the complexity of Colouring…